Preheat oven to 325F. Place butter, granulated sugar and vanilla in a mixing bowl. Use a pastry blender to combine butter and sugar until no large chunks of butter remain.
Add lemon zest, salt, coconut and all-purpose flour and continue using the pastry blender to combine until the mixture begins to form a dough that you can press together easily with your hands.
Divide the dough mixture in half. Take one half and use your hands to form a ball. Then place it on a lightly floured work surface and roll to 1/4 inch thick if using cookie cutters.
Use cutters to create shapes and use the excess dough to form a ball again and repeat the process. Then repeat with remaining 1/2 of the dough. Bake for 18-20 minutes.
Make a glaze. In a small bowl, use a fork to combine powdered sugar, lemon juice and a pinch of salt until smooth.